Month: March 2014

Categories
Math for Early Age /Elementary (G5 under)

On the Patterns -Elementary

★ On the Patterns

 

Number Patterns * Numbers, Colors and Stars

Taking a look at the following chart.

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The following questions are for everyone! Whether you are students in elementary schools (grade 3 and up), or in middle schools; or just parents who are tutoring your child; here are the challenges!

First, let us look up to the stars:

(1) What pattern is followed for the placement of stars ?

(2) Each number besides the star is increased by ____. (Fill in the blank)

(3) Following this pattern, the three more numbers that are besides and that comes after 58 are: __ , __ , and __.

(4) Now go back to the chart, and let us look at the colored cell (those colored by yellow)

(5) What can you do to follow the yellowed-colored cell? Please color the numbers on the chart by continue the pattern that you discovered.

(6) What are the common features of these yellow cells? Color some new cells, and explain how, by coloring these cells, you have followed and extended the pattern which is already in the chart.

Take a moment to think. You can answer these questions!

Categories
Geometry

3D objects with 3 views from top, front and side

For a 3D objects, given three views to you: one from top, one from front, and one from side, can you imagine what the original 3D objects looks like?

The question is not posed to a mechanic engineer, it would be trivial in that case. The question is raised to get a junior middle student to think a bit.

For a cylinder one of the three views is a circle, and the other two views are rectangles. For a cone one of the views is a circle, and the other two views are triangles. What if the three views given are a circle, a rectangle and a triangle? Can you figure out the original shape?

Categories
Geometry

Find the Center of a Circle — Do you know how to do it?

Using a compass, you can draw a circle at any place, with any radius.

Now let’s reverse the problem. Given a circle, do you know how to find its center? (Of course, once the circle is found, there shall be no problem at all to tell its diameter, or radius.) You only see the circle itself, there is no explicit indication on where the center is.

With two set of restrictions on what kind of tools you can use, there are actually two questions. In general, you can find the center using any convenient method, including copy-and-paste the circle onto a paper, and then fold it. In particular (from classical Euclidean geometry), where it’s required to do so with a ruler (with which you are allowed to draw lines and line segments only) and a compass (with which you are allowed to draw circles only).

See the following article on how to do it in general.

How to find the center of a given circle?

If you attempt to solve this problem with a ruler and a compass, then you are required to know how to make a perpendicular bisector. This will be discussed in another posting.